CFOUR | Main / Cholesky Decomposition

idea
N.H.F. Beebe and J. Linderberg, Simplifications in the generation and transformation of two‐electron integrals in molecular calculations, Int. J. Quant. Chem. 12, 683-705 (1977)

first serious realization (also implemented in CFOUR within the MINT integral package)
H. Koch, A.S. de Merás, T.B. Pedersen, Reduced scaling in electronic structure calculations using Cholesky decompositions, J. Chem. Phys. 118, 9481-9484 (2003)

efficient realizations (using a two-step procedure for the Cholesky decomposition; also available in CFOUR)
S.D. Folkestad, E.F. Kjønstad, H. Koch, An efficient algorithm for Cholesky decomposition of electron repulsion integrals, J. Chem. Phys. 150, 194112 (2019)

T. Zhang, X. Liu, E.F.Valeev, X. Li, Toward the Minimal Floating Operation Count Cholesky Decomposition of Electron Repulsion Integrals, J. Phys. Chem. A 125, 4258-4265 (2021)

realization with coupled-cluster and equation-of-motion coupled-cluster theory
E. Epifanovsky, D. Zuev, X. Feng, K. Khistayev, Y. Shao, A.I. Krylov, General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and qquation-of-motion methods: Theory and benchmarks, J. Chem. Phys. 139, 134105 (2013)

implementation in CFOUR with quadratically convergent SCF
T. Nottoli, J. Gauss, F. Lipparini, A black-box, general purpose quadratic self-consistent field code with and without Cholesky decomposition of the two-electron integrals, Mol. Phys. 119, e1974590 (2021)

implementation in CFOUR with CASSCF
T. Nottoli, J. Gauss, F. Lipparini, Second-order CASSCF algorithm with the Cholesky decomposition of the two-electron integrals, J. Chem. Theor. Comp. 17, 6819-6831 (2021)

implementation in CFOUR with CCSD
T. Nottoli, J. Gauss, F. Lipparini, A Novel Coupled-Cluster Singles and Doubles Implementation that Combines the Exploitation of Point- Group Symmetry and Cholesky Decomposition of the Two-Electron Integrals, J. Chem. Phys. 159, 231101 (2023)

implementation in CFOUR for relativistic two-component coupled-cluster methods

C. Zhang, F. Lipparini, S. Stopkowicz, J. Gauss, L. Cheng, Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules, J. Chem. Theor. Comp. 20, 787-798 (2023)

implementation in CFOUR for finite-magnetic-field calculations using GIAOs
S. Blaschke, S. Stopkowicz, Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields, J. Chem. Phys. 156, 044115 (2022)

J. Gauss, S. Blaschke, S. Burger, T. Nottoli, F. Lipparini,S. Stopkowicz, Cholesky decomposition of two-electron integrals in quantum-chemical calculations with perturbative or finite magnetic fields using gauge-including atomic orbitals, Mol. Phys. 121, e2101562 (2023)

geometrical gradients with Cholesky decomposition
X. Feng, E. Epifanovsky, J. Gauss, A.I. Krylov, Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks, J. Chem. Phys. 151, 014110 (2019)

geometrical gradients with Cholesky decomposition (non CFOUR implementation)
A.K. Schnack-Petersen, H. Koch, S. Coriani, E.F. Kjønstad, Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals, J. Chem. Phys. 156, 244111 (2022)

NMR chemical shifts with Cholesky decomposition (CD-GIAO-MP2)
S. Burger, F. Lipparini, J. Gauss, S. Stopkowicz, NMR chemical shift computations at second-order Møller–Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals, J. Chem. Phys. 155, 074105 (2021)

NMR chemical shifts with Cholesky decomposition (CD-GIAO-CASSCF)
T. Nottoli, S. Burger, S. Stopkowicz, J. Gauss, F. Lipparini, Computation of NMR shieldings at the CASSCF level using gauge-including atomic orbitals and Cholesky decomposition, J. Chem. Phys. 157, 084122 (2022)

Spin-Free Dirac-Coulomb calculations with Cholesky decomposition
T. Uhlirova, D. Cianchino, T. Nottoli, F. Lipparini, J. Gauss, Cholesky Decomposition in Spin-Free Dirac-Coulomb Coupled-Cluster Calcuations, J. Phys. A, accepted for pubication (2024)?